{"id":2729,"date":"2026-09-22T10:43:52","date_gmt":"2026-09-22T03:43:52","guid":{"rendered":"https:\/\/navi.edu.vn\/blog\/?p=2729"},"modified":"2026-09-22T10:43:52","modified_gmt":"2026-09-22T03:43:52","slug":"toan-lop-5-len-lop-6-nhung-cu-soc-dau-cap","status":"publish","type":"post","link":"https:\/\/navi.edu.vn\/blog\/toan-lop-5-len-lop-6-nhung-cu-soc-dau-cap\/","title":{"rendered":"To\u00e1n l\u1edbp 5 l\u00ean l\u1edbp 6: Nh\u1eefng c\u00fa s\u1ed1c \u0111\u1ea7u c\u1ea5p v\u00e0 c\u00e1ch chu\u1ea9n b\u1ecb t\u1eeb s\u1edbm"},"content":{"rendered":"

Nhi\u1ec1u ba m\u1eb9 kh\u00f4ng kh\u1ecfi ng\u1ee1 ng\u00e0ng khi th\u1ea5y con \u1edf ti\u1ec3u h\u1ecdc lu\u00f4n \u0111\u1ea1t \u0111i\u1ec3m 9, \u0111i\u1ec3m 10 nh\u01b0ng v\u1eeba b\u01b0\u1edbc ch\u00e2n v\u00e0o l\u1edbp 6 \u0111i\u1ec3m s\u1ed1 l\u1ea1i t\u1ee5t d\u1ed1c b\u1ea5t ng\u1edd<\/span>. S\u1ef1 h\u1ee5t h\u01a1i n\u00e0y kh\u00f4ng ph\u1ea3i do con l\u01b0\u1eddi hay k\u00e9m th\u00f4ng minh, m\u00e0 ch\u1ee7 y\u1ebfu v\u00ec “c\u00fa s\u1ed1c” khi chuy\u1ec3n t\u1eeb c\u00e1ch t\u00ednh to\u00e1n \u0111\u01a1n gi\u1ea3n \u1edf c\u1ea5p 1 sang t\u01b0 duy tr\u1eebu t\u01b0\u1ee3ng \u1edf c\u1ea5p 2<\/span>. C\u00f9ng NaviEdu \u0111i\u1ec3m qua nh\u1eefng thay \u0111\u1ed5i m\u1ea5u ch\u1ed1t c\u1ee7a m\u00f4n To\u00e1n l\u1edbp 5 l\u00ean l\u1edbp 6<\/b> v\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng c\u1ea7n chu\u1ea9n b\u1ecb \u0111\u1ec3 gi\u00fap con t\u1ef1 tin v\u1eefng b\u01b0\u1edbc \u0111\u1ea7u c\u1ea5p<\/span>!<\/span><\/p>\n

S\u1ef1 kh\u00e1c bi\u1ec7t l\u1edbn gi\u1eefa ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n Ti\u1ec3u h\u1ecdc v\u00e0 THCS<\/strong><\/h2>\n
\"S\u1ef1
S\u1ef1 kh\u00e1c bi\u1ec7t t\u1eeb To\u00e1n l\u1edbp 5 l\u00ean l\u1edbp 6 \u0111\u1ebfn ki\u1ebfn th\u1ee9c v\u00e0 c\u00e1ch h\u1ecdc, c\u00e1ch t\u01b0 duy<\/figcaption><\/figure>\n

1. Chuy\u1ec3n d\u1ecbch t\u1eeb t\u00ednh to\u00e1n \u0111\u01a1n gi\u1ea3n sang t\u01b0 duy tr\u1eebu t\u01b0\u1ee3ng<\/h3>\n
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    \u1ede b\u1eadc Ti\u1ec3u h\u1ecdc:<\/b> To\u00e1n h\u1ecdc ch\u1ee7 y\u1ebfu g\u1eafn li\u1ec1n v\u1edbi c\u00e1c con s\u1ed1 c\u1ee5 th\u1ec3, tr\u1ef1c quan th\u00f4ng qua c\u00e1c b\u00e0i to\u00e1n t\u00ednh to\u00e1n c\u01a1 b\u1ea3n (c\u1ed9ng, tr\u1eeb, nh\u00e2n, chia) v\u00e0 c\u00e1c d\u1ea1ng to\u00e1n th\u1ef1c t\u1ebf quen thu\u1ed9c nh\u01b0 b\u00e0i to\u00e1n t\u00ednh tu\u1ed5i, qu\u00e3ng \u0111\u01b0\u1eddng hay t\u00ecm hai s\u1ed1 khi bi\u1ebft t\u1ed5ng v\u00e0 t\u1ec9 s\u1ed1.<\/p>\n<\/li>\n

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    L\u00ean l\u1edbp 6:<\/b> Con b\u1eaft \u0111\u1ea7u l\u00e0m quen v\u1edbi c\u00e1c bi\u1ebfn s\u1ed1, c\u00e1c ch\u1eef c\u00e1i \u0111\u1ea1i di\u1ec7n cho s\u1ed1 (nh\u01b0 x, y, a, b) v\u00e0 t\u01b0 duy \u0111\u1ea1i s\u1ed1. Thay v\u00ec nh\u00ecn v\u00e0o nh\u1eefng con s\u1ed1 c\u00f3 s\u1eb5n \u0111\u1ec3 nh\u1ea9m k\u1ebft qu\u1ea3, h\u1ecdc sinh ph\u1ea3i t\u1eadp c\u00e1ch bi\u1ec3u di\u1ec5n c\u00e1c m\u1ed1i quan h\u1ec7 logic th\u00f4ng qua bi\u1ec3u th\u1ee9c, khi\u1ebfn nhi\u1ec1u em c\u1ea3m th\u1ea5y m\u00f4n h\u1ecdc tr\u1edf n\u00ean tr\u1eebu t\u01b0\u1ee3ng v\u00e0 kh\u00f3 h\u00ecnh dung h\u01a1n r\u1ea5t nhi\u1ec1u.<\/p>\n<\/li>\n<\/ul>\n

    2. Xu\u1ea5t hi\u1ec7n nh\u1eefng m\u1ea3ng ki\u1ebfn th\u1ee9c ho\u00e0n to\u00e0n m\u1edbi<\/h3>\n

    Ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 6 \u0111\u01b0a v\u00e0o nh\u1eefng kh\u00e1i ni\u1ec7m ch\u01b0a t\u1eebng c\u00f3 \u1edf c\u1ea5p 1, \u0111\u00f2i h\u1ecfi kh\u1ea3 n\u0103ng t\u01b0 duy \u0111a chi\u1ec1u:<\/p>\n

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      T\u1eadp h\u1ee3p s\u1ed1 nguy\u00ean:<\/b> Con kh\u00f4ng c\u00f2n ch\u1ec9 l\u00e0m vi\u1ec7c v\u1edbi c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean\u00a0m\u00e0 b\u1eaft \u0111\u1ea7u ti\u1ebfp c\u1eadn v\u1edbi s\u1ed1 nguy\u00ean \u00e2m, tr\u1ee5c s\u1ed1 v\u00e0 c\u00e1c quy t\u1eafc nh\u00e2n chia, quy t\u1eafc \u0111\u1ed5i d\u1ea5u. Ch\u1ec9 c\u1ea7n nh\u1ea7m l\u1eabn m\u1ed9t d\u1ea5u c\u1ed9ng +<\/span> ho\u1eb7c tr\u1eeb –<\/span> l\u00e0 to\u00e0n b\u1ed9 k\u1ebft qu\u1ea3 ph\u00eda sau s\u1ebd sai ho\u00e0n to\u00e0n.<\/p>\n<\/li>\n

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      L\u00fd thuy\u1ebft chia h\u1ebft v\u00e0 \u01b0\u1edbc – b\u1ed9i:<\/b> C\u00e1c d\u1ea1ng to\u00e1n v\u1ec1 t\u00ednh ch\u1ea5t chia h\u1ebft, \u01b0\u1edbc chung l\u1edbn nh\u1ea5t, b\u1ed9i chung nh\u1ecf nh\u1ea5t \u0111\u00f2i h\u1ecfi h\u1ecdc sinh ph\u1ea3i hi\u1ec3u s\u00e2u c\u1ea5u tr\u00fac c\u1ee7a m\u1ed9t s\u1ed1 v\u00e0 suy lu\u1eadn logic nhi\u1ec1u b\u01b0\u1edbc, ch\u1ee9 kh\u00f4ng c\u00f2n d\u1eebng l\u1ea1i \u1edf vi\u1ec7c t\u00ednh nh\u1ea9m ra \u0111\u00e1p s\u1ed1 nh\u01b0 \u1edf ti\u1ec3u h\u1ecdc.<\/p>\n<\/li>\n<\/ul>\n

      3. H\u00ecnh h\u1ecdc tr\u1ef1c quan chuy\u1ec3n sang y\u00eau c\u1ea7u l\u1eadp lu\u1eadn logic ch\u1eb7t ch\u1ebd<\/h3>\n
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        C\u00e1ch h\u1ecdc c\u0169 \u1edf c\u1ea5p 1:<\/b> H\u00ecnh h\u1ecdc ch\u1ee7 y\u1ebfu mang t\u00ednh \u0111o \u0111\u1ea1c, nh\u1eadn bi\u1ebft h\u00ecnh d\u1ea1ng v\u00e0 \u00e1p d\u1ee5ng tr\u1ef1c ti\u1ebfp c\u00e1c c\u00f4ng th\u1ee9c c\u00f3 s\u1eb5n \u0111\u1ec3 t\u00ednh chu vi, di\u1ec7n t\u00edch c\u00e1c h\u00ecnh quen thu\u1ed9c nh\u01b0 h\u00ecnh vu\u00f4ng, h\u00ecnh tam gi\u00e1c hay h\u00ecnh tr\u00f2n.<\/p>\n<\/li>\n

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        Y\u00eau c\u1ea7u m\u1edbi \u1edf l\u1edbp 6:<\/b> Con ph\u1ea3i l\u00e0m quen v\u1edbi c\u00e1c kh\u00e1i ni\u1ec7m tr\u1eebu t\u01b0\u1ee3ng h\u01a1n nh\u01b0 \u0111i\u1ec3m, \u0111\u01b0\u1eddng th\u1eb3ng, \u0111o\u1ea1n th\u1eb3ng, tia, g\u00f3c. Quan tr\u1ecdng h\u01a1n, con kh\u00f4ng \u0111\u01b0\u1ee3c “nh\u00ecn b\u1eb1ng m\u1eaft \u0111\u1ec3 \u0111o\u00e1n” m\u00e0 b\u1eaft bu\u1ed9c ph\u1ea3i gi\u1ea3i th\u00edch, l\u1eadp lu\u1eadn c\u00f3 c\u0103n c\u1ee9 (v\u00ed d\u1ee5: v\u00ec sao \u0111i\u1ec3m B<\/span> n\u1eb1m gi\u1eefa \u0111i\u1ec3m A<\/span> v\u00e0 C<\/span>, t\u1eeb \u0111\u00f3 m\u1edbi c\u00f3 ph\u00e9p c\u1ed9ng \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng). Vi\u1ec7c ph\u1ea3i di\u1ec5n \u0111\u1ea1t t\u1eebng b\u01b0\u1edbc logic th\u00e0nh l\u1eddi v\u0103n ch\u00ednh l\u00e0 m\u1ed9t trong nh\u1eefng tr\u1edf ng\u1ea1i l\u1edbn khi\u1ebfn c\u00e1c con d\u1ec5 b\u1ecb m\u1ea5t \u0111i\u1ec3m \u1edf h\u1ecdc k\u1ef3 \u0111\u1ea7u c\u1ea5p.<\/p>\n<\/li>\n<\/ul>\n

        Nh\u1eefng b\u1ee1 ng\u1ee1 khi\u1ebfn h\u1ecdc sinh d\u1ec5 b\u1ecb h\u1ee5t h\u01a1i ngay h\u1ecdc k\u1ef3 1 l\u1edbp 6<\/strong><\/h2>\n
        \"Vi\u1ec7c
        Vi\u1ec7c chuy\u1ec3n c\u1ea5p khi\u1ebfn nhi\u1ec1u con ch\u01b0a th\u1ec3 l\u00e0m quen v\u1edbi c\u00e1ch h\u1ecdc m\u1edbi d\u1eabn \u0111\u1ebfn vi\u1ec7c b\u1ecb t\u1ee5t l\u1ea1i<\/figcaption><\/figure>\n

        Kh\u00f4ng ch\u1ec9 c\u00f3 ki\u1ebfn th\u1ee9c kh\u00f3 l\u00ean, s\u1ef1 thay \u0111\u1ed5i to\u00e0n di\u1ec7n v\u1ec1 m\u00f4i tr\u01b0\u1eddng v\u00e0 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3ng d\u1ea1y \u1edf c\u1ea5p 2 c\u0169ng l\u00e0 nguy\u00ean nh\u00e2n khi\u1ebfn nhi\u1ec1u h\u1ecdc sinh d\u00f9 h\u1ecdc r\u1ea5t ch\u1eafc \u1edf ti\u1ec3u h\u1ecdc v\u1eabn b\u1ecb “s\u1ed1c” v\u00e0 t\u1ee5t \u0111i\u1ec3m nhanh ch\u00f3ng ngay trong h\u1ecdc k\u1ef3 \u0111\u1ea7u ti\u00ean:<\/p>\n

        1. T\u1ed1c \u0111\u1ed9 gi\u1ea3ng b\u00e0i nhanh h\u01a1n, l\u01b0\u1ee3ng b\u00e0i t\u1eadp d\u1ed3n d\u1eadp<\/h3>\n
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          Kh\u00f4ng c\u00f2n s\u1ef1 k\u00e8m c\u1eb7p t\u1eebng li t\u1eebng t\u00ed:<\/b> \u1ede c\u1ea5p 1, gi\u00e1o vi\u00ean ch\u1ee7 nhi\u1ec7m th\u01b0\u1eddng d\u1ea1y h\u1ea7u h\u1ebft c\u00e1c m\u00f4n, c\u00f3 nhi\u1ec1u th\u1eddi gian nh\u1eafc nh\u1edf v\u00e0 n\u1eafn n\u00f3t t\u1eebng b\u01b0\u1edbc cho t\u1eebng b\u1ea1n. B\u01b0\u1edbc l\u00ean l\u1edbp 6, m\u1ed7i m\u00f4n h\u1ecdc l\u00e0 m\u1ed9t th\u1ea7y c\u00f4 b\u1ed9 m\u00f4n ri\u00eang, ti\u1ebft h\u1ecdc ch\u1ec9 v\u1ecfn v\u1eb9n 45 ph\u00fat n\u00ean th\u1ea7y c\u00f4 b\u1eaft bu\u1ed9c ph\u1ea3i d\u1ea1y \u0111\u00fang ti\u1ebfn \u0111\u1ed9 ch\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<\/li>\n

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          Th\u1eddi gian tr\u00ean l\u1edbp tr\u00f4i qua r\u1ea5t nhanh:<\/b> N\u1ebfu con l\u01a1 \u0111\u00e3ng hay ch\u01b0a k\u1ecbp hi\u1ec3u m\u1ed9t c\u00f4ng th\u1ee9c, th\u1ea7y c\u00f4 kh\u00f3 c\u00f3 th\u1ec3 d\u1eebng l\u1ea1i c\u1ea3 ti\u1ebft h\u1ecdc \u0111\u1ec3 ch\u1edd m\u1ed9t v\u00e0i b\u1ea1n. C\u00f9ng l\u00fac \u0111\u00f3, b\u00e0i t\u1eadp v\u1ec1 nh\u00e0 c\u1ee7a nhi\u1ec1u m\u00f4n d\u1ed3n l\u1ea1i khi\u1ebfn con d\u1ec5 r\u01a1i v\u00e0o tr\u1ea1ng th\u00e1i qu\u00e1 t\u1ea3i, ng\u1ee3p v\u00e0 kh\u00f4ng theo k\u1ecbp nh\u1ecbp h\u1ecdc chung.<\/p>\n<\/li>\n<\/ul>\n

          2. C\u00e1ch ghi ch\u00e9p v\u00e0 k\u1ef9 n\u0103ng t\u1ef1 h\u1ecdc thay \u0111\u1ed5i ho\u00e0n to\u00e0n<\/h3>\n
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            Kh\u00f4ng c\u00f2n \u0111\u01b0\u1ee3c “\u0111\u1ecdc cho ch\u00e9p” hay ch\u00e9p b\u1ea3ng t\u1eebng ch\u1eef:<\/b> Th\u1ea7y c\u00f4 c\u1ea5p 2 th\u01b0\u1eddng gi\u1ea3ng b\u00e0i k\u1ebft h\u1ee3p ghi b\u1ea3ng t\u00f3m t\u1eaft, h\u1ecdc sinh ph\u1ea3i v\u1eeba nghe, v\u1eeba hi\u1ec3u v\u00e0 ch\u1ee7 \u0111\u1ed9ng l\u1ecdc ra \u00fd quan tr\u1ecdng \u0111\u1ec3 ghi v\u00e0o v\u1edf.<\/p>\n<\/li>\n

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            V\u1ec1 nh\u00e0 m\u1edf v\u1edf ra kh\u00f4ng bi\u1ebft \u00f4n t\u1eeb \u0111\u00e2u:<\/b> Ph\u1ea7n l\u1edbn c\u00e1c b\u1ea1n h\u1ecdc sinh m\u1edbi l\u00ean l\u1edbp 6 ch\u01b0a c\u00f3 k\u1ef9 n\u0103ng t\u1ef1 h\u1ecdc v\u00e0 ghi ch\u00e9p khoa h\u1ecdc. K\u1ebft qu\u1ea3 l\u00e0 v\u1edf ghi ch\u1ed7 thi\u1ebfu ch\u1ed7 th\u1eeba, v\u1ec1 nh\u00e0 nh\u00ecn v\u00e0o b\u00e0i t\u1eadp kh\u00f4ng nh\u1edb th\u1ea7y c\u00f4 \u0111\u00e3 h\u01b0\u1edbng d\u1eabn ph\u01b0\u01a1ng ph\u00e1p g\u00ec, d\u1eabn \u0111\u1ebfn vi\u1ec7c ng\u1ed3i loay hoay c\u1ea3 t\u1ed1i m\u00e0 kh\u00f4ng l\u00e0m xong b\u00e0i t\u1eadp v\u1ec1 nh\u00e0.<\/p>\n<\/li>\n<\/ul>\n

            3. Th\u00f3i quen l\u00e0m t\u1eaft, nh\u1ea9m nhanh b\u1ecb tr\u1eeb \u0111i\u1ec3m r\u1ea5t n\u1eb7ng<\/h3>\n